Captain reported multiple ECAM messages relating to Yellow Hydraulic System while at cruise. The flight crew requested priority handling and continued to the destination.

Narrative

During the cruise segment; the ECAM alerted with HYD Y RSVR OVHT; Y ENG 2 PUMP LO PR; & Y SYS LO PR in Amber. The ECAMs directed us to turn off the PTU and the Engine 2 Yellow Hydraulic Pump. We consulted the Flight Handbook and monitored the Brake Accumulator pressure for the remainder of the flight and determined that we would have the Parking Brake on Landing. The Status Page showed a number of associated systems had failed; including Nose Wheel Steering. We decided to [request priority handling] out of an abundance of caution; and contacted Dispatch via ACARS to tell them we would need to be towed off the runway after landing. We briefed the Flight Attendants; and made a PA informing the passengers of our situation. The remainder of the flight was uneventful. The OVHT condition went out passing about FL200 on the descent and the Status page directed us to select Eng 2 HYD Pump ON during approach. The Amber Fault light extinguished initially; but came on again soon after. We landed without incident; stopped straight ahead on the runway with a single; steady application of brakes and the Engine 1 Reverser. Once stopped; we set the parking brake with the Accumulator pressure; waited 3 minutes; and then shut down both engines. The Fire department inspected the Landing Gear and Brakes; gave us the 'All Clear;' and we were towed to the gate with the APU powering the aircraft systems.